Throughout this description various publications are cited as representative of related art. For the sake of simplicity, these documents will be referred by reference numbers enclosed in square brackets, e.g., [x]. A complete list of these publications ordered according to the reference numbers is reproduced in the section entitled “References” at the end of the description.
Wireless transmission through multiple antennas, also referred to as Multiple-Input Multiple-Output (MIMO) [1]-[2], currently enjoys great popularity because of the demand of high-data-rate communication from multimedia services.
Many applications are considering the use of MIMO to enhance the data rate and/or the robustness of the link; among others, a significant example is provided by the next generation of wireless LAN networks (W-LANs), see e.g., the IEEE 802.11n standard [3]. Another candidate application is represented by mobile “WiMax” systems for fixed wireless access (FWA) [4]-[5]. Besides fourth generation (4G) mobile terminals will likely endorse MIMO technology and as such represent a very important commercial application for embodiments of the present disclosure.
OFDM has been adopted in several high-speed wireless communication standards, mainly due to its capability to effectively combat Inter Symbol Interference (ISI), and to the high spectral efficiency achieved by spectrum overlapping through the adoption of a Fast Fourier Transformation (FFT).
In addition, the multi-path propagation typical of indoor environments can provide high capacities, if properly exploited. This can be achieved by employing multi-element antenna arrays at both the transmitter and the receiver side, hence creating a MIMO communication system.
Serial-Input Serial-Output (SISO), Serial-Input Multiple-Output (SIMO) and MIMO architectures often require accurate Channel State Information (CSI) at the receiver side to perform coherent detection.
Especially in orthogonal frequency division multiplexing (OFDM) communication systems paths between each transmitting and receiving antenna are estimated, for each OFDM subcarrier (tone) involved in the transmission process.
Systems based on a packet transmission, with the periodical insertion of a preamble, containing known sequences (called training sequences), allow synchronization and channel estimation at the beginning of each transmission.
A severe case is a MIMO indoor channel in which multiple reflections and spatial diversity may cause severe interference on the received signals, so that they channel has to be properly estimated and resolved to allow adequate reception.
The general concept of channel estimation in MIMO communication systems will be analyzed in the following, however the same principles apply also to SISO and SIMO communication systems.
MIMO-OFDM systems typically work in indoor environments, rich in obstacles, reflections and scattering.
For this reason, the link between each transmitting and receiving antenna includes multiple paths (called taps), each one with different gain and phase (consequence of a different time arrival to the receiver), resulting in channels with long power delay profiles (PDP), the power spread at the receiver of a hypothetical transmitted impulse h(t), defined as:PDP(t)=E[|h(t)|2]  (1)
This channel model takes into consideration the comparison criteria used, e.g., for the IEEE 802.11n standard [4].
This model foresees at least three degrees of randomness: uniformly distributed blocks of paths with casual exponentially decaying power, both between clusters and inside each cluster.
The higher the number of relevant taps, the lower the correlation between adjacent tones and vice versa.
In fact, in the case of a channel with ideal impulse response, its Fourier transform would be a constant, because each tone would be fully correlated with all other tones.
On the contrary, if the channel were made of Gaussian taps, equal to the number of FFT points, the correlation between two adjacent tones would be null, which is known as the condition of maximum frequency selectivity.
For example in a typical office environment large PDPs exist and adjacent tones appear highly correlated. Generally the correlation values between a first carrier n and second carrier spaced by m can be calculated according to:Rr1,t1,r2,t2(m)=E[hr1,t1*(n)hr2,t2(n+m)]  (2)
Generally, Channel Estimation (CE) can be performed either in the time or frequency domain [6], [10], [11].
One method exploits the knowledge of the channel impulse-response length, and generally guarantees better performance, at the cost of drastically higher computational complexity [6], [7].
Several methods have been proposed in the literature to improve the performances of channel estimation methods [8], [9], but usually the complexity of the solutions is not taken into account and they are not practical in a communication system.